PSYCHOPHYSICAL DISCRIMINATION 57 



tensity or its intensity relative to that of some other specified stimulus. 



We consider, then, parallel neurons or chains interconnected by 

 inhibitory neurons (Figure 1), and we impose here the further re- 

 strictions that their inhibitory effect is numerically the same as the 

 excitatory effect due to the neuron with the same origin. Then a stim- 

 ulus Sx may produce a response Ri , and S 2 a response R 2 , if the stim- 

 uli are presented separately. But if the stimuli are presented to- 

 gether, then the response R x will be produced if S x exceeds S 2 by an 

 amount which depends upon the thresholds of the efferent neurons. 

 If the difference between S x and S 2 is too small, neither response oc- 

 curs. If the thresholds are negligibly small, the response R x occurs 

 alone if 5 1 > S, and R 2 if S 2 > S 1 . 



Because of fluctuations of the type discussed in the preceding 

 chapter, the values of s-l and e 2 produced by the afferent neurons will 

 not generally be exactly equal even when S x = S 2 . If S t is slightly 

 greater than S 2 , there is a certain finite probability, less than one- 

 half, that the response R 2 will be given instead of Ri , the probability 

 decreasing as the difference between S x and S 2 is increased. 



Suppose that fluctuations occur only in the thresholds of the 

 afferent neurons. The fluctuation of the threshold of any neuron 

 causes fluctuation of the o- produced by this neuron, and we shall pos- 

 tulate the distribution of o- rather than that of h . Furthermore, be- 

 cause of the interconnections between the neurons, an increase in o- 

 at the terminus of one afferent has the same effect as a decrease in a 

 at the other, so that formally we may regard the fluctuation as oc- 

 curring at only one synapse (Landahl, 1943). Thus we shall assume 

 that the thresholds are constant but that at synapse s x , <r — e — j + C 

 where s and j result from the activity of the afferents but C is nor- 

 mally distributed about zero. 



We shall assume that the net is completely symmetrical. Let h' 

 be the threshold of either efferent. As we are assuming that y and b 

 of the interconnecting inhibitory neurons are equal to <£ and a of the 

 parallel excitatory neurons, a 1 = e 3 — j\ = — a 2 = — (e 4 — y 3 ). Thus 

 o-i and (7 2 are equal and opposite. Using equation (6) of chapter i, we 

 may write the stationary values as 



Si 



ax — - a 2 = p\0g— . (1) 



Now a! exceeds h' if the stimulus S-l exceeds S 2 sufficiently. But then 

 e, will exceed e 2 by some value h . We may summarize as follows: 



If e r — e 2 — C > h , response Ri is given ; 



